Question

given the congruence statement, solve for x
△pqr≅△mnr

Explanation:

Step1: Recall congruent - triangle property

Corresponding angles of congruent triangles are equal. In \(\triangle PQR\cong\triangle MNR\), \(\angle QPR=\angle NMR = 35^{\circ}\).

Step2: Use angle - sum property of a triangle

In right - triangle \(PQR\), \(\angle QPR + \angle PQR+\angle PRQ=180^{\circ}\), and \(\angle PQR = 90^{\circ}\). Also, \(\angle PRQ=x^{\circ}\). So \(x = 180-(90 + 35)\).

Step3: Calculate the value of \(x\)

\(x=180 - 125=55\).

Answer:

\(x = 55\)